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      SUBROUTINE <a name="DDISNA.1"></a><a href="ddisna.f.html#DDISNA.1">DDISNA</a>( JOB, M, N, D, SEP, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      CHARACTER          JOB
      INTEGER            INFO, M, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      DOUBLE PRECISION   D( * ), SEP( * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="DDISNA.18"></a><a href="ddisna.f.html#DDISNA.1">DDISNA</a> computes the reciprocal condition numbers for the eigenvectors
</span><span class="comment">*</span><span class="comment">  of a real symmetric or complex Hermitian matrix or for the left or
</span><span class="comment">*</span><span class="comment">  right singular vectors of a general m-by-n matrix. The reciprocal
</span><span class="comment">*</span><span class="comment">  condition number is the 'gap' between the corresponding eigenvalue or
</span><span class="comment">*</span><span class="comment">  singular value and the nearest other one.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  The bound on the error, measured by angle in radians, in the I-th
</span><span class="comment">*</span><span class="comment">  computed vector is given by
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">         <a name="DLAMCH.27"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>( 'E' ) * ( ANORM / SEP( I ) )
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  where ANORM = 2-norm(A) = max( abs( D(j) ) ).  SEP(I) is not allowed
</span><span class="comment">*</span><span class="comment">  to be smaller than <a name="DLAMCH.30"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>( 'E' )*ANORM in order to limit the size of
</span><span class="comment">*</span><span class="comment">  the error bound.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="DDISNA.33"></a><a href="ddisna.f.html#DDISNA.1">DDISNA</a> may also be used to compute error bounds for eigenvectors of
</span><span class="comment">*</span><span class="comment">  the generalized symmetric definite eigenproblem.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  JOB     (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          Specifies for which problem the reciprocal condition numbers
</span><span class="comment">*</span><span class="comment">          should be computed:
</span><span class="comment">*</span><span class="comment">          = 'E':  the eigenvectors of a symmetric/Hermitian matrix;
</span><span class="comment">*</span><span class="comment">          = 'L':  the left singular vectors of a general matrix;
</span><span class="comment">*</span><span class="comment">          = 'R':  the right singular vectors of a general matrix.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  M       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of rows of the matrix. M &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          If JOB = 'L' or 'R', the number of columns of the matrix,
</span><span class="comment">*</span><span class="comment">          in which case N &gt;= 0. Ignored if JOB = 'E'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  D       (input) DOUBLE PRECISION array, dimension (M) if JOB = 'E'
</span><span class="comment">*</span><span class="comment">                              dimension (min(M,N)) if JOB = 'L' or 'R'
</span><span class="comment">*</span><span class="comment">          The eigenvalues (if JOB = 'E') or singular values (if JOB =
</span><span class="comment">*</span><span class="comment">          'L' or 'R') of the matrix, in either increasing or decreasing
</span><span class="comment">*</span><span class="comment">          order. If singular values, they must be non-negative.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  SEP     (output) DOUBLE PRECISION array, dimension (M) if JOB = 'E'
</span><span class="comment">*</span><span class="comment">                               dimension (min(M,N)) if JOB = 'L' or 'R'
</span><span class="comment">*</span><span class="comment">          The reciprocal condition numbers of the vectors.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INFO    (output) INTEGER
</span><span class="comment">*</span><span class="comment">          = 0:  successful exit.
</span><span class="comment">*</span><span class="comment">          &lt; 0:  if INFO = -i, the i-th argument had an illegal value.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      DOUBLE PRECISION   ZERO
      PARAMETER          ( ZERO = 0.0D+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            DECR, EIGEN, INCR, LEFT, RIGHT, SING
      INTEGER            I, K
      DOUBLE PRECISION   ANORM, EPS, NEWGAP, OLDGAP, SAFMIN, THRESH
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.79"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      DOUBLE PRECISION   <a name="DLAMCH.80"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>
      EXTERNAL           <a name="LSAME.81"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="DLAMCH.81"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          ABS, MAX, MIN
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="XERBLA.87"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Test the input arguments
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      EIGEN = <a name="LSAME.94"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOB, <span class="string">'E'</span> )
      LEFT = <a name="LSAME.95"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOB, <span class="string">'L'</span> )
      RIGHT = <a name="LSAME.96"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOB, <span class="string">'R'</span> )
      SING = LEFT .OR. RIGHT
      IF( EIGEN ) THEN
         K = M
      ELSE IF( SING ) THEN
         K = MIN( M, N )
      END IF
      IF( .NOT.EIGEN .AND. .NOT.SING ) THEN
         INFO = -1
      ELSE IF( M.LT.0 ) THEN
         INFO = -2
      ELSE IF( K.LT.0 ) THEN
         INFO = -3
      ELSE
         INCR = .TRUE.
         DECR = .TRUE.
         DO 10 I = 1, K - 1
            IF( INCR )
     $         INCR = INCR .AND. D( I ).LE.D( I+1 )
            IF( DECR )
     $         DECR = DECR .AND. D( I ).GE.D( I+1 )
   10    CONTINUE
         IF( SING .AND. K.GT.0 ) THEN
            IF( INCR )
     $         INCR = INCR .AND. ZERO.LE.D( 1 )
            IF( DECR )
     $         DECR = DECR .AND. D( K ).GE.ZERO
         END IF
         IF( .NOT.( INCR .OR. DECR ) )
     $      INFO = -4
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.128"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="DDISNA.128"></a><a href="ddisna.f.html#DDISNA.1">DDISNA</a>'</span>, -INFO )
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span>      IF( K.EQ.0 )
     $   RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Compute reciprocal condition numbers
</span><span class="comment">*</span><span class="comment">
</span>      IF( K.EQ.1 ) THEN
         SEP( 1 ) = <a name="DLAMCH.140"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>( <span class="string">'O'</span> )
      ELSE
         OLDGAP = ABS( D( 2 )-D( 1 ) )
         SEP( 1 ) = OLDGAP
         DO 20 I = 2, K - 1
            NEWGAP = ABS( D( I+1 )-D( I ) )
            SEP( I ) = MIN( OLDGAP, NEWGAP )
            OLDGAP = NEWGAP
   20    CONTINUE
         SEP( K ) = OLDGAP
      END IF
      IF( SING ) THEN
         IF( ( LEFT .AND. M.GT.N ) .OR. ( RIGHT .AND. M.LT.N ) ) THEN
            IF( INCR )
     $         SEP( 1 ) = MIN( SEP( 1 ), D( 1 ) )
            IF( DECR )
     $         SEP( K ) = MIN( SEP( K ), D( K ) )
         END IF
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Ensure that reciprocal condition numbers are not less than
</span><span class="comment">*</span><span class="comment">     threshold, in order to limit the size of the error bound
</span><span class="comment">*</span><span class="comment">
</span>      EPS = <a name="DLAMCH.163"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>( <span class="string">'E'</span> )
      SAFMIN = <a name="DLAMCH.164"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>( <span class="string">'S'</span> )
      ANORM = MAX( ABS( D( 1 ) ), ABS( D( K ) ) )
      IF( ANORM.EQ.ZERO ) THEN
         THRESH = EPS
      ELSE
         THRESH = MAX( EPS*ANORM, SAFMIN )
      END IF
      DO 30 I = 1, K
         SEP( I ) = MAX( SEP( I ), THRESH )
   30 CONTINUE
<span class="comment">*</span><span class="comment">
</span>      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="DDISNA.177"></a><a href="ddisna.f.html#DDISNA.1">DDISNA</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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